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A Note on the $S_2(\delta)$ Distribution and the Riemann Xi Function

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A Note on the $S_2(\delta)$ Distribution and the Riemann Xi Function
2.	Creator	Author's name, affiliation, country	Dmitry Ostrovsky; Independent researcher; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Riemann xi function; Mellin transform; Laplace transform; Functional equation; Infinite divisibility
3.	Subject	Subject classification	11M06; 30D05; 30D10; 60E07; 60E10
4.	Description	Abstract	The theory of $S_2(\delta)$ family of probability distributions is used to give a derivation of the functional equation of the Riemann xi function. The $\delta$ deformation of the xi function is formulated in terms of the $S_2(\delta)$ distribution and shown to satisfy Riemann's functional equation.  Criteria for simplicity of roots of the xi function and for its simple roots to satisfy the Riemann hypothesis are formulated in terms of a differentiability property of the $S_2(\delta)$ family. For application, the values of the Riemann zeta function at the integers and of the Riemann xi function in the complex plane are represented as integrals involving the Laplace transform of $S_2.$
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-12-11
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/3608
10.	Identifier	Digital Object Identifier	10.1214/ECP.v19-3608
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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